This article proposes a novel monolithic compliant spatial
parallel XY stage (SPXYS). An important feature of the SPXYS lies in that it
can deliver centimeter travel range and sustain large out-of-plane payload
while possessing a compact structure, which makes the SPXYS suitable for some
special applications such as Ultra-Violet Nanoimprint Lithography and
soft-contact lithography. Different from conventional compliant positioning
stages, the proposed SPXYS consists of a monolithic spatial parallel linear
compliant mechanism (SPLCM) driven by four matching designed voice coil
motors (VCMs). The moving platform of the stage is connected to the base by
four spatial prismatic-prismatic (PP) joints, which are enveloped from planar
PP joint based on the position space reconfiguration (PSR) method to realize
desired travel range, payload capacity and compact size. The mechatronic
model of the SPXYS is established by integrated using matrix structural
analysis (MSA) and the method of images. The design flow chart of the SPXYS
is given based on the key parameter sensitivity analysis. Furthermore, a
reified SPXYS is designed and manufactured. The analytical design of the
stage is confirmed by experiments. The reified stage has a travel range of
20.4 × 20.6 mm2, a compact structure with area ratio
1.87 %, and the resonant frequencies of the two working modes at 22.98
and 21.31 Hz. It can track a circular trajectory with the radius of 4.5 mm.
The root mean squares (RMS) tracking error is 2 µm. The positioning
resolution is 100 nm. The payload capacity test shows that the reified stage
can bear 20 kg out-of-plane payload.

Compliant positioning stages (CPSs) possess many merits, such as reduced
number of parts, no friction, no backlash and free of lubrication (Howell,
2001; Smith, 2000), which make them have extensive applications such as micro
manufacturing, optical fiber alignment, biological engineering, scanning
probe microscopy (SPM) and lithography (Yong et al., 2012; Kenton et al.,
2012; Chen et al., 1992; Muthuswamy et al., 2002). But some special
applications such as Ultra-Violet Nanoimprint Lithography (UV-NIL) and
soft-contact lithography (Teo, 2014; Qu, 2014) expect that the CPS has not
only large travel range, but also large out-of-plane payload carrying
capacity without any other auxiliary supporting equipment. Moreover,
restrained by space limitation, compact mechatronic design of CPS is usually
expected. Hence, this article is concentrated on the design and development
of a compliant XY position stage which has large travel range, compact
structure, high out-of-plane payload capacity and matching design of voice
coil motors (VCMs).

Parallel XY stage (PXYS) is the most common layout of XY stages because of
its advantages including identical dynamic features in working axes, low
inertia, and low cumulative positioning errors (Teo, 2014). In order to
obtain parallel XY stages with large travel and compact size, leaf spring
parallelograms are widely used as prismatic (P) joints. Normally, leaf
spring parallelograms are used in couples forming a PP joint to realize
kinematically decoupling. According to whether the leaf springs are in the
plane of motion or normal to the plane of motion, PP joints can be divided
into two types: planar and spatial PP joints. Parallel XY stages using planar
or spatial PP joints are defined as planar parallel XY stages (PPXYSs) or
spatial parallel XY stages (SPXYSs) in this article.

PPXYSs are the most common XY stages because of its easy manufacturability.
In order to obtain large travel of PPXYS, much interest has been focused on
structural design. A large number of millimeter-scale PPXYSs were proposed by
researchers. Awtar (2004), Trease et al. (2004), Tang et al. (2006),
Xu (2012) and Yu et al. (2015) have designed and developed millimeter even
centimeter scale PPXYSs. However, there are two main defects of these PPXYSs:
(a) the structures of the stages are relatively loose. It is challenging to
design an XY stage with a large workspace and a compact physical dimension,
simultaneously. Using the modified area ratio (Xu, 2012) whose denominators
the actuators' dimensions should be added into, the area ratios of the stages
proposed in Awtar (2004), Xu (2012) and Yu et al. (2015) are only about
0.067, 0.069 and 0.026 % respectively; (b) the out-of-plane payload
capacity is weak. When applied large out-of-plane payload, the
load-stiffening phenomenon (Awtar et al., 2007) emerges in PPXYSs, which
would induce nonlinearity and cause the loss of travel range.

Researchers have been trying to develop a large travel range PXYS with
compact size and high out-of-plane payload simultaneously. By stacking two
identical planar XY stages, Xu (2014) has tried to use cubical space to
obtain large travel and compact size. The area ratio of the stage is
significantly improved to 0.13 % and the out-of-plane payload capacity is
indeed increased. But the actuation force is also increased by 14 % and
the nonlinearity of the stage becomes obvious in the whole travel range.
Nevertheless, Xu pointed a possible direction using the cubical space to meet
the above conflicting requirements. Since spatial PP joint has the remarkable
supporting capacity in the length direction of the leaf spring, Hao (2011), Hao and
Kong (2012) and Shang et al. (2015) have figured out using the combination of
spatial parallelograms and planar compliant joints to enhance the
out-of-plane stiffness. The out-of-plane stiffness is enhanced indeed, but
the Shang's stage suffers from relatively short travel range and low area
ratio (only 0.002 %) because the spatial parallelogram used in the stage
is lumped compliance parallelogram. The stage proposed by Hao and Kong (2012)
meets the requirement of large travel range (20 × 20 mm motion
range), compact structure (area ratio: 0.14 %) and high out-of-plane
payload capacity. But the structural configuration of the stage is too
complex to be fabricated monolithically. Therefore, the stage should be an
assembly which would induce the assemble error.

Due to the merits of large stroke, no friction and vacuum compatibility, VCM
is widely used in CPSs. Therefore, besides the spatial parallel linear
compliant mechanism (SPLCM), VCM directly influences the compactness of CPSs.
For example, the stage proposed by Xu (2014) actually has a reachable
workspace of 20 × 20 mm2 with the area ratio of 2.78 %.
However, constrained by the commercial VCM, the actual workspace is only
about 11.75 × 11.66 mm2 and the area ratio drops to only about
0.13 %. Kang et al. (2009) proposed a compact XY scanner with specially
designed voice coil motors (VCMs) and leaf springs. The VCMs were embedded in
the stage to make the stage compact. However, the supporting structure
comprised an assembly of leaf springs, thereby introducing assembly error and
deteriorating positioning accuracy. Hence, the matching design VCM is adopted
in this paper to achieve the goal of compact size and the VCM and SPLCM
should be co-designed in the fully consideration of the coupling
relationships between the actuators and the supporting structure.

Inspired by the aforementioned researcher's work, a novel SPXYS is presented
in this article. Different from conventional compliant positioning stages,
the proposed SPXYS consists of a monolithic SPLCM driven by four matching
designed VCMs. The moving platform of the stage is connected to the base by
four spatial PP joints, which are enveloped from planar PP joint based on the
position space reconfiguration (PSR) method to realize desired centimeter
travel range, compact structure, as well as high out-of-plane payload
capacity. The matching designed VCMs further ensure the structural
compactness. For the sake of realizing the co-design process of the VCM and
SPLCM, the design mechatronic model of VCMs matching for the SPXYS, which
describes the coupling relationships between the actuators and the supporting
structure, is derived by integrated using matrix structural analysis (MSA)
and the method of images. The integrated design flow chart including both
mechanical and electromagnetic of the whole SPXYS is given based on the key
parameter sensitivity analysis. Furthermore, a reified SPXYS is designed and
manufactured. The analytical design of the stage is confirmed by experiments.
The reified stage has a travel range of 20.4 × 20.6 mm2, a
compact structure with area ratio 1.87 %, and the resonant frequencies of
the two working modes at 22.98 and 21.31 Hz. It can track a circular
trajectory with the radius of 4.5 mm. The root mean squares (RMS) tracking
error is 2 µm. The positioning resolution is 100 nm. The payload
capacity test shows that the reified stage can bear 20 kg out-of-plane
payload. The designed SPXYS is suitable for precision positioning
applications, such as Ultra-Violet Nanoimprint Lithography (UV-NIL) and
soft-contact lithography, which expect a compact compliant positioning stage
has not only large travel range, but also large out-of-plane payload carrying
capacity without any other auxiliary supporting equipment.

The rest of the article is organized as follows: In Sect. 2, the conceptual
design of the SPXYS is introduced based on the kinematic substitution and
position spaces method. In Sect. 3, the whole mechatronic model of the
proposed SPXYS is derived. In Sect. 4, the integrated design flow chart is
established and a reified SPXYS is realized. Performances discussion is
conducted by FEA analysis and a series of experiments involving static
performance test, dynamic performance test, out-of-plane payload capacity
test and tracking performance test in Sect. 5, followed by conclusions in
Sect. 6.

The SPXYS can be obtained based on the kinematic substitution and position
spaces method (Hao et al., 2016; Li and Hao, 2016; Li et al., 2016). The
conceptual design procedure starts from the design of a rigid body 4-PP
decoupled parallel mechanism as shown in Fig. 1. Each PP leg is composed of
two P joints in series. The outer P joint connected to the base is
actuated and the inner one is passive joint as a decoupler. The motion
directions of the two adjacent P joints are perpendicular to each other to
achieve kinematical decoupling, which is the necessary condition for
two-axis XY parallel mechanisms.

The second step is to replace each traditional P joints in the above rigid
body 4-PP decoupled parallel mechanism (Fig. 1) with certain appropriate
compliant P joints. In order to increase the motion range, alleviate the
cross-axis coupling and geometric stiffening effects, planar double leaf
spring parallelograms are selected to construct the basic compliant
P joints. Two basic compliant P joints combined together to construct a
PP decoupled compliant block.

With the goal to produce a compact and monolithic XY compliant stage with the
smallest possible size in length and width directions, an improved spatial PP
decoupled compliant block (S-PP-DCB) is derived with position spaces
concept from the frequently-used planer PP decoupled compliant block
(P-PP-DCB). Each P joint in the P-PP-DCB can be simplified to a
“black straight line”, one end point of which is fixed while another end
point of which has a translation, TP,
represented by a “blue straight line”. The position space of the P joint
is designated as a “red circle” about its translation, TP as shown
in Fig. 2. One can identify the most compact PP compliant block with smallest
size along its guiding axis and its decoupling axis by arranging
PG parallel to PD. The compliant block is
termed S-PP-DCB due to that PG, PD,
TG, TD are not coplanar.

A compact and monolithic fabrication XY positioning stage with large
translational travel range and high out-of-plane payload capacity can be
produced by combining four S-PP-DCBs, four voice coil motors (VCMs) and two
optical linear encoders, as shown in Fig. 3. It can be termed as SPXYS due to
the S-PP-DCBs. The mechanical structure of the SPXYS composed of four
S-PP-DCBs can be named as spatial parallel linear compliant mechanism
(SPLCM). The VCMs are specially designed according to the structure of the
SPLCM for compact size, instead of using the existing commercial VCMs to meet
the requirements of travel range, peak force and conformity with the inner
structure of the SPLCM simultaneously. In order to reduce the number of motor
drivers, the two VCMs on the pair of opposite sides of the SPLCM are parallel
connected to the same motor driver. Each parallel connected VCM pair provides
translational actuating force along guiding axis and some rotational
constraint damping along XYZ axes that can suppress the unwanted angular
vibration caused by high order rotational modes along XYZ axes without any power consumption. The optical scales of
the linear grating encoders are fixed at the intermediate platforms instead
of the moving platform and still capable of measuring the position of the
moving platform precisely, which is verified in Hao (2017).

3.1 SPLCM modeling

The stiffness characteristic of compliant mechanism has direct effects on the
workspace, load-carrying capacity, dynamic behavior and positioning accuracy
of the entire mechanism (Zhu et al., 2015). The mathematical model of SPLCM
is established by Matrix of structural analysis (MSA) (Przemieniecki, 1968).
There are four guiding leaf spring flexures and four decoupling leaf spring
flexures in each S-PP-DCB. These leaf springs, guiding beams and three
platforms form two guiding parallelograms and two basic decoupling
parallelograms, denoted as S1–S4, which is shown in Fig. 4a. Details about
definitions of the dimensions and coordinate of each parallelogram are shown
in Fig. 4b–d.

Each S-PP-DCB can be viewed as four basic parallelograms connected in
series. The details of the derivation are already shown in Liu et al. (2017).
The relationship of the displacement δs at the center of the
platform and the external force Fe as
well as the actuator forces Fai is:

where Tlsj is the transformation matrix from jth
basic parallelogram coordinate to the leg coordinate,
Ksj
is the stiffness of the jth basic parallelogram,
Tlis is the transformation matrix from the
moving platform to the ith leg, Tasi is the
transformation matrix of the ith parallelogram with respect to the location
of the actuation force. Actually, the second item on the right-hand side of
Eq. (1) is the equivalent external force Fae generated by
actuation force Fai, which is in form of:

(2)Fae=∑i=14TlisT∑j=14TlsjKsj-1TlsjT-1∑j=12TlsjKsj-1TasjTFai.

When the actuator forces Fai are equal to zero,
the stiffness of the stage related to the displacement δs at
the center of the platform and the external force Fe is

(3)Ks=∂Fe∂δs=∑i=14TlisT∑j=14TlsjKsj-1TlsjT-1Tlis.

According to Liu et al. (2017), the displacement δasi of
the ith leg at the actuator point caused by the external force
Fe is

According to Eq. (6), the unexpected displacement of one actuator caused by
another actuator, the actuator isolation expressed in form of the input
coupling displacement (Jiang et al., 2015), δ̃ai-y, can be obtained. Based on which, the clearance between
the coil and stator of the VCM can be determined.

Meanwhile, the transmission performance from the actuator to the moving
platform, named as lost motion, can be obtained by the difference
displacement between the actuation point and the moving platform in Eqs. (5)
and (6).

According to the Lagrange's equation, the natural resonant frequencies of
the stage can be obtained as follows:

(7)f=12πKsM,

where M is the mass matrices in which the mass of the VCMs' movers
is also included, M= diag {Mx, My, Mz, Jx,
Jy, Jz} and Mx=My, Jx=Jy because of the symmetric
structure of the stage.

Since Ks is the function of structure parameters of the stage,
the relationship between structural parameter and resonant frequencies can be
revealed similarly by numerical method.

3.2 VCM modeling

VCMs are selected as the actuators because of their large travel range,
lubrication-free property, and vacuum compatibility. The VCM adopted in this
article is designed in a dual permanent magnet (PM) configuration as shown in
Fig. 5a. The specific dimensions of the actuator are shown in Fig. 5b and c.
In order to reach the full travel range of the SPLCM, the dimensions of the
VCM should meet the following constraints:

(8)La≥2b+2Δp+ly+bgWa=2aTa=2ly+2lm+lg2b≥lca+2.2Sa+2Δb-2Δp,

where La, Wa and Ta are the length, width
and thickness of the VCM's stator; 2a, 2b and lm are the
length, width and thickness of the PM, respectively; bg is the
width of the guiding leaf spring; ly and lg are the
thickness of the yoke and the air gap; lca is the axial length of
the coil; Δp is the clearance between the permanent magnet
and the yoke; Δb is the thickness of the bobbin.

Accordance with the conservation of magnetic flux, the constraint of the
yoke's thickness that the yoke's thickness should be larger than the
saturated thickness can be expressed as

(9)ly≥Bg⋅2b2Bs

Since the permeability of the yoke of the VCM is relatively high and the
configuration of the VCM is symmetric, the method of images is used to obtain
the analytical model of the gap's field (Furlani, 2001) and the equivalent
magnetic structure is shown in Fig. 5d. The vertical component
Bgz of the gap magnetic flux density due to equivalent
PM1 with the dimension of
2a× 2b× 2lm shown in Fig. 5d is provided
in Eq. (10).

where Ms represent the magnetization, and μ0 is the
magnetic permeability of air,

(11)gx,y,z;xn,ym,zk=1x-xn2+y-ym2+z-zk2xm=-1m⋅byk=-1k⋅lmzn=-1n⋅a

According to the magnetic symmetry of a single PM, the vertical component
Bgz of the gap magnetic field at the point A (x, y, z)
due to PM2 is equal to the value of the
gap magnetic field at point A′(x, y,
z-lg-2lm) due to PM1. Hence the vertical component Bgzs
generated by the two PMs is

(12)Bgzs=Bgzx,y,z+Bgzx,y-lg-2lm,z

The effective coil length, lce, is related to the width of PM,
Wa, and the number of turns in the coil,
nl×nc, and is expressed as:

(13)lce=nl⋅nc⋅Wa

where nl is the layer number of the coil, and nc is
the number of turns per layer of the coil, given as

(14)nl=fix2(lg-Δg)+(3-2)dw3dwnc=fix(lca/dw)

In Eq. (14), dw is the diameter of the wire, Δg
is the clearance between the coil and the stator which should be carefully
designed according to Eq. (5), in case the coil contacts with the stator.
lca is the axial length of the coil and fix(x) is the rounding
function for the numeric value x.

Hence, the Lorentz force fi generated by the ith VCM is

(15)fi=Bgzs⋅ii⋅lceii=1,⋯,4

where ii and lcei is the current and effective length of
the ith coil in the gap.

Section 3 focused on the mechatronic modeling of the SPXYS including both the
SPLCM and VCMs, while this section mainly concentrates on illustrating how to
design the SPXYS by establishing a design flow chart and an example case
study. The desired key performance indicators of the reified example SPXYS
are tabulated in Table 1.

4.1 Design constraints

4.1.1 Geometric constraint

In order to obtain high area ratio, the actuators in the stage are
conformal-designed and make the most of the inner space of the SPLCM. The
design area of the VCM, namely the geometric coupling relationship, is shown
in Fig. 6.

Since the VCM used in the stage is linear motor, the stator has to be in a
rectangle shape. Hence, the stator of the VCM should be designed within the
following dimensions:

(16)La≤bg+Dgd+2Dd+Ds-bd/2Wa≤Lg-2Δb-2lgTa≤Dgd+Dd-Δs

where Δs is the clearance between the stator and the outer
guiding leaf spring, which is intended to provide enough space for the outer
guiding leaf spring's maximum deflection, Sa∕2, and given as

(17)Δs≥Sa/2+tg-ly+3.5

4.1.2 Performance constraint

Besides the geometric coupling relationships, there are some coupling
relationships associated with the performances of the SPLCM and VCMs
including the key performances listed in Table 1 and the secondary
performances (e.g., the driving force, stiffness, actuator isolation and
moving mass of the stage), which is depicted in Fig. 7. The key performances
normally depend on the secondary performances, while the secondary
performances are directly related to the design parameters.

Key performances

Since the out-of-plane payload is sustained by the leaf spring in its length
direction, the dimensions of guiding and decoupling leaf springs have direct
effect on the out-of-plane payload capacity. The out-of-plane payload
capacity of the stage depends on the critical buckling load of secondary
parallelograms of guiding or decoupling parallelograms, namely S2 or S4 in
Fig. 5. There are eight leaf springs of guiding or decoupling parallelograms
under compressive load, so the maximum out-of-plane payload
PL max is limited by the minor one, given as

(18)PLmax≤min⁡2π2EIz(g)nstLg2,2π2EIz(d)nstLd2

where E is the Young's modulus, Iz is the Z-axial area moment of
inertia and equal to bt3/12, nst is the safety factor,
normally over 2, Lg and Ld is the lengths of the
guiding and decoupling leaf springs.

The length of the stage, according to the specific dimensions in Fig. 4, is

(19)Lx=Ly=2bg+2Dgd+4Dd+2Ds+2.2Sa

Hence, the area ratio of the stage is given as:

(20)Ra=4Sa2/2bg+2Dgd+4Dd+2Ds+2.2Sa2

The relationship of the resonant frequency fr with the stiffness
Ks and moving mass M has been clearly illustrated in
Eq. (7).

Secondary performance

The travel range Sa depends on the driving force Fa
and the stiffness Ks according to Eq. (5). The maximum driving
force Fa_max needed in the stage should be larger than the sum
of elastic force and inertia force. The maximum driving force
Fa_max provided by the actuator is determined by the gap
magnetic flux density Bgz, the effective length lce
and the maximum current imax, which associates with all the
independent parameters of the actuator.

The stiffness, cross-axis coupling, lost motion and actuator isolation are
depended on all of the independent parameters of the SPLCM.

The actuator isolation should be taken into special consideration in
designing the actuator. The clearance Δg between the coil
and stator should be two or three times larger than the input coupling
displacement δ̃ai-y, that is,

(21)Δg≥(3∼4)δ̃ai-y

In the contrast, the clearance Δg should be as small as
possible during the actuator design according to Eq. (14), so that it can
make the coil as long as possible and obtain as large driving force as
possible.

4.1.3 Other constraints

In order to ensure the linearity of the stage, the small deflection
condition should be satisfied by choosing appropriate length L of the leaf
spring as follows

(22)L≥10ymax⁡=5Sa

where ymax is the maximum deflection of each leaf spring,
ymax=Sa/2.

Based on the maximal shear theory, the thickness t of the leaf spring is
given by

(23)t≤2σyL23SfEymax⁡=4σyL23SfESa

where σy is the yeilding stress, Sf is the safe factor.

4.2 Sensitivity analysis and design flow chart

Since the relationships between design parameters and performances are
relatively complicated, it is necessary to analyze the sensitivities of the
key design parameters. The independent design parameters in the SPLCM are
investigated to verify their influences on the primary performances since the
independent design parameters of the VCM are constrained within the design
domain. The design parameters of the VCM would be determined to maximize the
driving force by means of the genetic algorithms. The variation ranges and
relationships of the design parameters are presented in Table 2.

Table 2Variation ranges and relationships of the design parameters of the
stage.

The initial values of the parameters of the stage are the respective medians
of their variation ranges. The boundary limits of each parameter are
normalized into [0, 1]. The normalized parametric analysis (Xu, 2014) results
of SPLCM and VCM are presented in Fig. 8.

As shown in Fig. 8, the change trends of travel range and area ratio are
almost identical, whereas the change trends of travel range Sa
and resonant frequency fr are opposite. Therefore, design optimization
should maximize one performance indicator on the premise of ensuring the
sufficiency of the others. The three most important parameters influencing
the travel range, area ratio and resonant frequency of the stage are the
length and thickness of the leaf spring and the distance between the guiding
and decoupling parallelograms; while the three most important parameters for
out-of-plane payload are the length, width and thickness of the leaf springs.
Among the parameters, the most sensitive parameters are the length and
thickness of the leaf springs; the secondary parameter is the distance
between the guiding and decoupling parallelograms; then the width of the leaf
springs and lastly the rest of the parameters. Hence, the design of the stage
should begin with the parameters, which have the clear relationship with the
design goals, and try to meet the design goals as much as possible and adjust
the parameters in accordance with the sensitivity descending order until the
design goals are all satisfied. The specific design flow chart of the stage
is shown in Fig. 9.

4.3 Parameter determination of reified SPXYS

According to the proposed design procedure and manufacturability
requirements, the travel range Sa is designed to 10 mm (a total
motion range is 20 mm), and the other parameters of the structure are
designed as the results in Table 3. The dimensions of the stage are
150 × 150 × 86 mm3. The material of the stage is
aluminum alloy (7075-T6) with Young's modulus
E=7.2× 1010 Pa, yield strength
σy=5.05× 108 Pa, density ρ=2810 kg m−3. And the PMs are the NdFeB (type: N50M) with the
residual magnetic flux density of 1.41 T.

In order to verify the analytical model and inspect the characteristics of
the proposed SPXYS, a series of FEA and experimental studies on four primary
performances tests as well as the secondary performances, e.g., the
stiffness and actuator isolation, have been carried out.

The prototype of the SPXYS was fabricated by two main working procedures:
milling process and wire electrodischarge machine (wire-EDM). The large
stress generated by the milling process led to serious deformations of leaf
springs during the wire-EDM process. The actual thicknesses of the
prototype's leaf springs listed in Table 4 are quite different with the
design value.

Hence, in order to verify the correctness of the theoretical model and
eliminate the influence of the manufacturing error, the analytical and FEA
models adopt the actual thickness in this section. The analytical and FEA
performances are in good agreements with each other as tabulated in Table 5,
which indicates that the theoretical model is validated.

Figure 10 shows the experimental setups for the stiffness and motion
characteristic tests of the SPXYS. In the stiffness test, a contact
displacement sensor (Mitutoyo LGF-110L) with resolution 1 µm and a
strain pressure transducer (VISTE VS16) with resolution 0.5 N is utilized to
measure the displacement and force experienced by the moving platform while
the micrometer is used as a loader to generate force and displacement. In the
motion characteristics test, two linear grating encoders (MicroE Systems
Mercury II 6500) with 50 nm resolution are used as the semi-closed loop
sensors measuring the displacement of the intermediate platform. And two
types of the external laser displacement sensors (Keyence LB72: 20 mm
measuring range with the repeatability 2 µm and LK-G30: 10 mm
measuring range with the repeatability 50 nm) are utilized to obtain the
lost motion between the moving and intermediate platform and verify the
position precision of the stage, respectively. A semi-practical simulation
system of dSPACE (ds1103) is utilized as a precise controller, which acquires
the feedback data of sensors and outputs control commands.

5.1 Static performance test

In order to verify the correctness of the theoretical modeling, the static
performances of the stage, such as stiffness, travel range, lost motion,
actuator isolation and area ratio would be tested first.

The stiffness test results and the curve fitting results obtained by the
method of linear least square (LLS) are shown in Fig. 11. The experimental
errors with respect to theoretical stiffness are less than 1.5 %, which
further indicates that the stiffness modeling is correct.

The test results of travel range, lost motion and actuator isolation, as well
as area ratio were obtained by applying a triangle-wave signal with amplitude
of 10 V to the VCMs. Only one axis is under driven and the other one is set
free. As Fig. 12a shown, the non-load travel ranges of the SPXYS in X-axis
direction and Y-axis direction are 20.4 and 20.6 mm and the design target of
travel range is realized, which further confirm the correctness of
theoretical modeling. The stage possesses planar dimensions of
150 × 150 mm2. Thus, the area ratio of the stage is
1.87 %, which is the most compact stage among related works.

As shown in Fig. 12b, the maximum cross-axis coupling displacement is about
0.04 mm, which indicates that the stage is well decoupled. Besides, the
cross-axis coupling relationship can be depressed by adopting decoupling
control. The maximum lost motions shown in Fig. 12c are less than 2 % of
the travel range, and X-axial lost motion is a little larger than that of
Y-axis, which may be caused by the stiffness difference in the two axes.
The maximum input coupling displacement, representative of actuator
isolation, in Fig. 12d are 0.266 mm and 0.267 mm and meets the design
constraint in Eq. (23).

5.2 Dynamic performance test

To investigate the dynamic performance of the developed stage, a chirp signal
with amplitude of 1V and frequency ranging from 0.1 to 200 Hz is applied to
the VCM. The inputs are denoted as Vx and Vy (in volts), and the
outputs are Dx and Dy (in millimeters). The frequency responses of
Gxx=Dx/Vx, Gxy=Dy/Vx, Gyx=Dx/Vy and
Gyy=Dy/Vy are shown in Fig. 13. So, Gxy and Gyx
represent for the dynamic coupling of the stage.

The two working mode resonant frequency of the stage is 22.98 and
21.31 Hz in X-axis and Y-axis respectively, which is close to the
theoretical and FEA results with the error about 10 %. The dynamic
responses of the moving platform and intermediate platform are almost
identical before 60 Hz, which indicates that the decoupling leaf spring has
relative large transmission stiffness and paves the way of half-closed loop
control. Figure 13 shows that the magnitudes of the coupling terms Gxy
and Gyx are about 40 dB less than that of Gxx and Gyy,
which are small enough to be neglected and indicate kinematic decoupling of
the stage. The close loop bandwidth (−3 dB) of the stage is 60.5 Hz in
the two working directions.

5.3 Out-of-plane payload capacity test

In order to determine the out-of-plane payload capacity, a variety of
payloads (0–20 kg) were applied on the load clamp and the results are
depicted in Fig. 14a and b. Figure 14c is a test photo of 20 Kg out-of-plane
payload. As the load increases, the travel ranges of the two working axes
slightly change, which sufficiently implies that SPXYS has high out-of-plane
payload capacity and could meet the payload requirements of UV-NIL's
positioning stage. The flat curves at the ends of the test curves, which are
also found in the travel range test shown in Fig. 12a, are caused by the
structural limitations of both SPLCM and VCMs. The stiffness of the stage
slightly decreases with the increment of the payloads, which makes it easy
for the VCMs to drive the moving platform to reach the max travel range and
causes the longer flat curves.

5.4 Tracking performance test

To further study the positioning characteristics of the stage, the tracking
performance and resolution of the stage are tested by applying a circular
trajectory and a consecutive step, respectively. The tracking trajectory is a
circle of radius 4.5 mm at the frequency of 0.1 Hz, as shown in Fig. 15. It
is noted that the stage can follow the large travel range command with the
RMS (root of mean square) tracking errors about 0.98 and 1.6 µm in
X-axis and Y-axis, which makes it superiority in large travel precision
applications. The trajectory of the moving platform is non-circular inside of
the intermediate platform's trajectory, which may be caused by the different
lost motions of the two axes and the coordinate misalignment between the
measuring block and the stage.

Figure 16 shows the experimental results of the 100 nm consecutive steps
positioning, which indicates that the positioning resolution is about
100 nm.

A novel monolithic compliant spatial parallel XY stage with centimeter travel
range, compact size and high out-of-plane payload capacity has been proposed.
The mechatronic model of the whole SPXYS involving both SPLCM and VCMs is
derived for mechanism and electromagnetic matching design. The integrated
design flow chart is established and a reified SPXYS is realized for case
study. It can be concluded from both the analytical and experimental results
that, the prototype of the SPXYS has a large range of motion up to
20.4 × 20.6 mm with a relatively compact structure only
150 × 150 mm, which makes the area ratio of the stage about
1.87 %. The stage exhibits a relatively high precision including
well-constraint cross-axis decoupling displacement less than 0.04 mm, and
acceptable lost motion below 2 % of the primary motion. The stage also
shows a good dynamic characteristic with the resonant frequencies about 22.98
and 21.31 Hz along X-axis and Y-axis, and a capability of sustaining
about 20 Kg out-of-plane payload without decreasing the travel range, which
makes it superiority in space-limited precision applications with high
payload capability requirement. The developed stage exhibits a good
capability of tracking a circle of radius 4.5 mm with RMS tracking error of
2 µm and possessing a relatively high resolution of 100 nm.

This research is supported by National Basic Research Program of China (973
Program, Grant No. 2015CB057503) and National Natural Science Foundation of
China (Grant No. 61405256, No. 51575423). The authors would like to thank the
reviewers for their excellent comments and suggestions.

Muthuswamy, J., Salas, D., and Okandan, M.: A chronic micropositioning system
for neurophysiology, Engineering in Medicine and Biology, 2002, Conference
and the Fall Meeting of the Biomedical Engineering Society Embs/bmes
Conference, Proceedings of the Second Joint, 2113, 2115–2116, https://doi.org/10.1109/IEMBS.2002.1053195, 2002.

This article proposes a novel monolithic compliant spatial parallel XY stage (SPXYS). An important feature of the SPXYS lies in that it can deliver centimeter travel range and sustain large out-of-plane payload while possessing a compact structure, which makes the SPXYS suitable for some special applications such as Ultra-Violet Nanoimprint Lithography and soft-contact lithography.